There is a regional train to Apolda once an hour. We took the train from Weimar which only took a few minutes. The one way ticket cost Euro 3.30 (March 2009).
We were quite surprised that there were no luggage lockers in the railway station. When the ticket counter/snack corner is open you may leave your luggage there but on a Saturday there were limited opening hours so we had no option but to drag our suitcase trolleys behind us on our sightseeing tour through the town and over cobbles stones.
The station building dates back to 1889 and is built in new Renaissance style. The original station from 1846 had burnt down.
Unfortunately, there is only one train per hour in each direction.
There are also buses eg to Weimar. The central bus station is in the town center.
Apolda is a good starting point for hiking trips. You can follow the way of Napoleon who was defeated nearby or visit all the small villages around to get an impression of Thuringian flair.
Here are some suggested routes:
Intercity stop in Weimar or Jena (Thur.)
Frankfurt/Main - Eisenach (Thur.) - Erfurt (airport via Munich) - Weimar - Apolda - Naumburg - Halle (Saale) [or via Leipzig (Sachsen/Saxonia)] - Berlin.